This invention is an improvement over U.S. Pat. No. 4,129,909 granted to Rhiel on Dec. 19, 1978. Rhiel discloses an appliance having pockets therein for the storage of articles. Rhiel comprises a sheet-like unitary member that reaches across and beyond the width of a bed so that pockets in the member hang along both sides of the bed. Its specification describes and its FIGURES illustrate various ways or embodiments by or in which storage pockets are found in the unitary member, and adapted for hanging along the sides of a bed. However, none of Rhiel's ways or embodiments show embodiments or ways of such an apparel or accessory that includes a pocket assembly or arrangement having distinct or separate layer or leafs or leaves of pocket means operatively connected together, with the outermost ones having the capability of being flippable back upon the apparel or accessory itself to expose to the eye another layer or leaf of pocket means. The outermost layer or leaf is connected to the apparel or accessory in a manner that hides the mouth of and the layer or leaf of pocket means immediately under it. The inventive concept begins with a pair pocket assemblies or arrangements along one or the other of or at both termini of a unitary member, the pocket means in each of the plurality of pocket assemblies or arrangements along one or both bedsides facing outwardly, yet only the exteriorly disposed one of the assemblies or arrangements with its pocket means being visibly exposed and the other or others under it are hidden to the eye.